{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "o4JZ84moBKMr",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Differentiable Fluid Simulations with Φ<sub>Flow</sub>\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/docs/Fluids_Tutorial.ipynb)\n",
    "\n",
    "This notebook steps you through setting up fluid simulations and using TensorFlow's differentiation to optimize them.\n",
    "\n",
    "Execute the cell below to install the [Φ<sub>Flow</sub> Python package from GitHub](https://github.com/tum-pbs/PhiFlow)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "Z6YoAVKebfNV",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# !pip install --quiet phiflow\n",
    "from phi.flow import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BVV1IKVqDfLl",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Setting up a Simulation\n",
    "\n",
    "Φ<sub>Flow</sub> is vectorized but object-oriented, i.e. data are represented by Python objects that internally use tensors.\n",
    "\n",
    "First, we create grids for the quantities we want to simulate. For this example, we require a velocity field and a smoke density field.\n",
    "We sample the smoke field at the cell centers and the velocity in [staggered form](https://tum-pbs.github.io/PhiFlow/Staggered_Grids.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "MA62qshHGcsk",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "smoke = CenteredGrid(0, extrapolation.BOUNDARY, x=32, y=40, bounds=Box(x=32, y=40))  # sampled at cell centers\n",
    "velocity = StaggeredGrid(0, extrapolation.ZERO, x=32, y=40, bounds=Box(x=32, y=40))  # sampled in staggered form at face centers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OTmqFIH5FBhp",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Additionally, we want to add more smoke every time step.\n",
    "We create the `INFLOW` field from a circle (2D [`Sphere`](https://tum-pbs.github.io/PhiFlow/phi/geom/index.html#phi.geom.Sphere)) which defines where hot smoke is emitted.\n",
    "Furthermore, we are interested in running the simulation for different inflow locations.\n",
    "\n",
    "Φ<sub>Flow</sub> supports data-parallell execution via *batch dimensions*.\n",
    "When a quantity has a batch dimension with size *n*, operations involving that quantity will be performed *n* times simultaneously and the result will also have that batch dimension. Here we add the batch dimension `inflow_loc`.\n",
    "\n",
    "For an overview of the dimension types, see the [documentation](https://tum-pbs.github.io/PhiFlow/Math.html#shapes)\n",
    "or watch the [introductory tutorial video](https://youtu.be/4nYwL8ZZDK8)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "WrA3IXDxv31P",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "INFLOW_LOCATION = tensor([(4, 5), (8, 5), (12, 5), (16, 5)], batch('inflow_loc'), channel(vector='x,y'))\n",
    "INFLOW = 0.6 * CenteredGrid(Sphere(center=INFLOW_LOCATION, radius=3), extrapolation.BOUNDARY, x=32, y=40, bounds=Box(x=32, y=40))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "oH7okuZUbVS-",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The created grids are instances of the class `Grid`.\n",
    "Like tensors, grids also have the `shape` attribute which lists all batch, spatial and channel dimensions.\n",
    "[Shapes in Φ<sub>Flow</sub>](https://tum-pbs.github.io/PhiFlow/Math.html#shapes) store not only the sizes of the dimensions but also their names and types."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "eK7T8Pdua5hh",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Smoke: (xˢ=32, yˢ=40)\n",
      "Velocity: (xˢ=32, yˢ=40, vectorᶜ=x,y)\n",
      "Inflow: (inflow_locᵇ=4, xˢ=32, yˢ=40)\n",
      "Inflow, spatial only: (xˢ=32, yˢ=40)\n"
     ]
    }
   ],
   "source": [
    "print(f\"Smoke: {smoke.shape}\")\n",
    "print(f\"Velocity: {velocity.shape}\")\n",
    "print(f\"Inflow: {INFLOW.shape}\")\n",
    "print(f\"Inflow, spatial only: {INFLOW.shape.spatial}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1S88yUJKa86i",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The grid values can be accessed using the `values` property."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "lHrsSzG2bMKq",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001B[92m(xˢ=32, yˢ=40)\u001B[0m \u001B[93mfloat32\u001B[0m const \u001B[94m0.0\u001B[0m\n",
      "\u001B[92m(xˢ=(x=\u001B[94m31\u001B[0m, y=\u001B[94m32\u001B[0m), yˢ=(x=\u001B[94m40\u001B[0m, y=\u001B[94m39\u001B[0m), vectorᶜ=x,y)\u001B[0m \u001B[93mfloat32\u001B[0m const \u001B[94m0.0\u001B[0m\n",
      "\u001B[92m(inflow_locᵇ=4, xˢ=32, yˢ=40)\u001B[0m \u001B[93mfloat32\u001B[0m  \u001B[94m0.015 ± 0.094\u001B[0m \u001B[37m(0e+00...6e-01)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "print(smoke.values)\n",
    "print(velocity.values)\n",
    "print(INFLOW.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "R8z7PWI_d2zM",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Grids have many more properties which are documented [here](https://tum-pbs.github.io/PhiFlow/phi/field/#phi.field.Grid).\n",
    "Also note that the staggered grid has a [non-uniform shape](https://tum-pbs.github.io/PhiFlow/Math.html#non-uniform-tensors) because the number of faces is not equal to the number of cells."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dWo_m_hYKZxM",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Running the Simulation\n",
    "\n",
    "Next, let's do some physics!\n",
    "Since the initial velocity is zero, we just add the inflow and the corresponding buoyancy force.\n",
    "For the buoyancy force we use the factor `(0, 0.5)` to specify strength and direction.\n",
    "Finally, we project the velocity field to make it incompressible.\n",
    "\n",
    "Note that the `@` operator is a shorthand for resampling a field at different points. Since `smoke` is sampled at cell centers and `velocity` at face centers, this conversion is necessary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "IZdJygJAKtNl",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 864x360 with 8 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "smoke += INFLOW\n",
    "buoyancy_force = smoke * (0, 0.5) @ velocity\n",
    "velocity += buoyancy_force\n",
    "velocity, _ = fluid.make_incompressible(velocity)\n",
    "\n",
    "vis.plot(smoke)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gvNzcYkyLU5o",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's run a longer simulation!\n",
    "Now we add the transport or *advection* operations to the simulation.\n",
    "Φ<sub>Flow</sub> provides multiple algorithms for advection.\n",
    "Here we use semi-Lagrangian advection for the velocity and MacCormack advection for the smoke distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "-9MEio1eK5Ic",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 "
     ]
    },
    {
     "data": {
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       "AC1pbHN0AAAAJal0b28AAAAdZGF0YQAAAAEAAAAATGF2ZjU4Ljc3LjEwMA==\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x24d649b0070>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trajectory = [smoke]\n",
    "for i in range(20):\n",
    "  print(i, end=' ')\n",
    "  smoke = advect.mac_cormack(smoke, velocity, dt=1) + INFLOW\n",
    "  buoyancy_force = smoke * (0, 0.5) @ velocity\n",
    "  velocity = advect.semi_lagrangian(velocity, velocity, dt=1) + buoyancy_force\n",
    "  velocity, _ = fluid.make_incompressible(velocity)\n",
    "  trajectory.append(smoke)\n",
    "trajectory = field.stack(trajectory, batch('time'))\n",
    "vis.plot(trajectory, animate='time')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rdSTbMoaS0Uz",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Obtaining Gradients\n",
    "\n",
    "The simulation we just computed was using pure NumPy so all operations were non-differentiable.\n",
    "To enable differentiability, we need to use either PyTorch, TensorFlow or Jax.\n",
    "This can be achieved by changing the import statement to [`phi.tf.flow`](https://tum-pbs.github.io/PhiFlow/phi/tf/flow.html), [`phi.torch.flow`](https://tum-pbs.github.io/PhiFlow/phi/torch/flow.html) or [`phi.jax.flow`](https://tum-pbs.github.io/PhiFlow/phi/jax/index.html), respectively.\n",
    "Tensors created after this import will be allocated using PyTorch / TensorFlow / Jax and operations on these will be executed with the corresponding backend.\n",
    "These operations can make use of a GPU through CUDA if your configuration supports it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "background_save": true
    },
    "id": "4vxomnHQT1y4",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# from phi.jax.flow import *\n",
    "from phi.torch.flow import *\n",
    "# from phi.tf.flow import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FgE9QbjvT7d7",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We set up the simulation as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "background_save": true
    },
    "id": "mphMP0sYIOz-",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "INFLOW_LOCATION = tensor([(4, 5), (8, 5), (12, 5), (16, 5)], batch('inflow_loc'), channel(vector='x,y'))\n",
    "INFLOW = 0.6 * CenteredGrid(Sphere(center=INFLOW_LOCATION, radius=3), extrapolation.BOUNDARY, x=32, y=40, bounds=Box(x=32, y=40))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GeeUQIQjf9_b",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We can verify that tensors are now backed by TensorFlow / PyTorch / Jax."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "VYZ1um3Of8_r",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "torch.Tensor"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(INFLOW.values.native(INFLOW.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3mpyowRYUSS4",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Note that tensors created with NumPy will keep using NumPy/SciPy operations unless a TensorFlow tensor is also passed to the same operation.\n",
    "\n",
    "Let's look at how to get gradients from our simulation.\n",
    "Say we want to optimize the initial velocities so that all simulations arrive at a final state that is similar to the right simulation where the inflow is located at `(16, 5)`.\n",
    "\n",
    "To achieve this, we define the loss function as $L = | D(s - s_r) |^2$ where $s$ denotes the smoke density and the function $D$ diffuses the difference to smoothen the gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "EPPzC6fTkN9n",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def simulate(smoke: CenteredGrid, velocity: StaggeredGrid):\n",
    "  for _ in range(20):\n",
    "    smoke = advect.mac_cormack(smoke, velocity, dt=1) + INFLOW\n",
    "    buoyancy_force = smoke * (0, 0.5) @ velocity\n",
    "    velocity = advect.semi_lagrangian(velocity, velocity, dt=1) + buoyancy_force\n",
    "    velocity, _ = fluid.make_incompressible(velocity)\n",
    "  loss = math.sum(field.l2_loss(diffuse.explicit(smoke - field.stop_gradient(smoke.inflow_loc[-1]), 1, 1, 10)))\n",
    "  return loss, smoke, velocity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KzHC3EGhk2Yr",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now it is important that the initial velocity has the `inflow_loc` dimension before we record the gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "ZKJ8NElOijxE",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "initial_smoke = CenteredGrid(0, extrapolation.BOUNDARY, x=32, y=40, bounds=Box(x=32, y=40))\n",
    "initial_velocity = StaggeredGrid(math.zeros(batch(inflow_loc=4)), extrapolation.ZERO, x=32, y=40, bounds=Box(x=32, y=40))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "O7iIylnIlC3F",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Finally, we use `gradient_function()` to obtain the gradient with respect to the initial velocity. Since the velocity is the second argument to the `simulate()` function, we pass `wrt=[1]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "hucSiIvjiv55",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "sim_grad = field.functional_gradient(simulate, wrt='velocity', get_output=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "V7ceJAc_lVIp",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The argument `get_output=False` specifies that we are not interested in the actual output of the function. By setting it to `True`, we would also get the loss value and the final simulation state.\n",
    "\n",
    "To evaluate the gradient, we simply call the gradient function with the same arguments as we would call the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "F8GMmTsdi7Mv",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 4 Axes>"
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 4 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "velocity_grad = sim_grad(initial_smoke, initial_velocity)\n",
    "\n",
    "vis.plot(velocity_grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IGt5l4JW2Hin",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "With the gradient, we can easily perform basic gradient descent optimization.\n",
    "For more advanced optimization techniques and neural network training, see the [optimization documentation](https://tum-pbs.github.io/PhiFlow/Optimization.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "iaAgH6Y3D4bT",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial loss: \u001B[94m(268.389, 214.372, 136.681, 0.000)\u001B[0m along \u001B[92minflow_locᵇ\u001B[0m\n",
      "Next loss: \u001B[94m(274.485, 239.472, 200.311, 0.000)\u001B[0m along \u001B[92minflow_locᵇ\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "print(f\"Initial loss: {simulate(initial_smoke, initial_velocity)[0]}\")\n",
    "initial_velocity -= 0.01 * velocity_grad\n",
    "print(f\"Next loss: {simulate(initial_smoke, initial_velocity)[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "YJe3qiLwD6OE",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 0, loss: \u001B[94m(274.485, 239.472, 200.311, 0.000)\u001B[0m along \u001B[92minflow_locᵇ\u001B[0m\n",
      "Step 1, loss: \u001B[94m(220.293, 177.165, 122.866, 0.000)\u001B[0m along \u001B[92minflow_locᵇ\u001B[0m\n",
      "Step 2, loss: \u001B[94m(216.114, 184.631, 82.620, 0.000)\u001B[0m along \u001B[92minflow_locᵇ\u001B[0m\n",
      "Step 3, loss: \u001B[94m(275.776, 183.743, 109.231, 0.000)\u001B[0m along \u001B[92minflow_locᵇ\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "sim_grad = field.functional_gradient(simulate, wrt='velocity', get_output=True)\n",
    "\n",
    "for opt_step in range(4):\n",
    "  (loss, final_smoke, _v), velocity_grad = sim_grad(initial_smoke, initial_velocity)\n",
    "  print(f\"Step {opt_step}, loss: {loss}\")\n",
    "  initial_velocity -= 0.01 * velocity_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ooqVxCPM8PXl",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "This notebook provided an introduction to running fluid simulations in NumPy and TensorFlow.\n",
    "It demonstrated how to obtain simulation gradients which can be used to optimize physical variables or train neural networks.\n",
    "\n",
    "The full Φ<sub>Flow</sub> documentation is available at [https://tum-pbs.github.io/PhiFlow/](https://tum-pbs.github.io/PhiFlow/).\n",
    "\n",
    "Visit the [playground](https://colab.research.google.com/drive/1zBlQbmNguRt-Vt332YvdTqlV4DBcus2S#offline=true&sandboxMode=true) to run Φ<sub>Flow</sub> code in an empty notebook."
   ]
  },
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   "source": []
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